Talk by Jorg Lucke of FIAS. Given to the Redwood Center for Theoretical Neuroscience at UC Berkeley.
In the nervous system of humans and animals, sensory data are represented as combinations of elementary data components. While for data such as sound waveforms the elementary components combine linearly, other data can better be modelled by non-linear forms of component superpositions. I motivate and discuss two models with binary latent variables: one using standard linear superpositions of basis functions and one using non-linear superpositions. Crucial for the applicability of both models are efficient learning procedures. I briefly introduce a novel training scheme (ET) and show how it can be applied to probabilistic generative models. For linear and non-linear models the scheme efficiently infers the basis functions as well as the level of sparseness and data noise. In large-scale applications to image patches, we show results on the statistics of inferred model parameters. Differences between the linear and non-linear models are discussed, and both models are compared to results of standard approaches in the literature and to experimental findings. Finally, I briefly discuss learning in a recent model that takes explicit component occlusions into account.